Classical hidden Markov chains (HMC) can be inefficient in the unsupervised segmentation of non stationary data. To overcome such involvedness, the more elaborated triplet Markov chains (TMC) resort to using an auxiliary underlying process to model the behavior switches within the hidden states process. However, so far, only this latter was considered non stationary. The aim of this paper is to extend the results of a recently proposed TMC by considering both hidden states and noise non stationary. To show the efficiency of the proposed model, we provide results of non stationary synthetic and real images restoration